Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp+(r-1)^G(i) the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r ...Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp+(r-1)^G(i) the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of (r - 1)G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp+(r-1)^G(i)∪(r - 1)K1 (1 ≤i≤p). Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.展开更多
In conventional isochronous mass spectrometry(IMS)performed on a storage ring,the precision of mass measurements for short-lived nuclei depends on the accurate determination of the revolution times(T)of stored ions.Ho...In conventional isochronous mass spectrometry(IMS)performed on a storage ring,the precision of mass measurements for short-lived nuclei depends on the accurate determination of the revolution times(T)of stored ions.However,the resolution of T inevitably deteriorates due to the magnetic rigidity spread of the ions,limiting the mass-resolving power.In this study,we used the betatron tunes Q(the number of betatron oscillations per revolution)of the ions and established a correlation between T and Q.From this correlation,T was transformed to correspond to a fixed Q with higher resolution.Using these transformed T values,the masses of ^(63)Ge,^(65)As,^(67)Se,and ^(71)Kr agreed well with the mass values measured using the newly developed IMS(Bρ-IMS).We also studied the systematics of Coulomb displacement energies(CDEs)and found that anomalous staggering in CDEs was eliminated using new mass values.This method of T transformation is highly effective for conventional IMS equipped with a single time-of-flight detector.展开更多
For positive integers k and r,a(k,r)-coloring of graph G is a proper vertex k-coloring of G such that the neighbors of any vertex v∈V(G)receive at least min{d_(G)(v),r}different colors.The r-hued chromatic number of ...For positive integers k and r,a(k,r)-coloring of graph G is a proper vertex k-coloring of G such that the neighbors of any vertex v∈V(G)receive at least min{d_(G)(v),r}different colors.The r-hued chromatic number of G,denoted χ_(r)(G),is the smallest integer k such that G admits a(k,r)-coloring.Let Q_(n) be the n-dimensional hypercube.For any integers n and r with n≥2 and 2≤r≤5,we investigated the behavior of χ_(r)(Q_(n)),and determined the exact value of χ_(2)(Q_(n))and χ_(3)(Q_(n))for all positive integers n.展开更多
Background:In this study,we explored the effects of different processing methods on the quality of Polygonatum cyrtonema Hua(PC),and the role of Huangjiu in the processing procedure.Methods:The sensory characteristics...Background:In this study,we explored the effects of different processing methods on the quality of Polygonatum cyrtonema Hua(PC),and the role of Huangjiu in the processing procedure.Methods:The sensory characteristics of the crude product,steamed product,and wine-processed product of PC were described.The colorimeter was used to analyze the chromatic values of three different processed products on PC.At the same time,the contents of the water extract and alcohol extract were measured separately.The content of three different processing Polygonatum Polysaccharide(PCP)was determined using 0.2%anthrone-sulfuric acid.The correlation difference between the chromatic values and chemical composition of different PC products was analyzed using various analytical methods.Results:The surface colors gradually deepened,the sweetness increased,the viscosity strengthened,and the tongue-numbing sensation disappeared after PC processing.The contents of extract and L^(*) gradually decreased from the crude to the steamed to the wine-processed product,consistent with the pattern of surface color alteration.While,E^(*)ab gradually increased.The content of PCP was crude product>wine-processed product>steamed product.The results of multivariate statistical analysis showed that the samples processed for crude,steamed,and wine-processed product were clustered into three classes.The correlation analysis showed that L^(*)and E^(*)ab were highly significant positively correlated with the content of PCP,and a*was significantly negatively correlated with the content of PCP.Conclusion:The results showed that the wine-processed product had the best quality.The internal quality of the PC was correlated with its characteristics and chromatic value.In this study,we investigated the internal and external quality of three different products of PC in order to provide a reference for further research on the impact of different processing methods on PC quality,the standardization of PC processing,and the role of Huangjiu in the processing of PC.展开更多
With the intensification of market competition in the aluminum alloy strip processing industry,it is dif-ficult to control the mass production of the same specifications,which is bound to affect the hot rolling produc...With the intensification of market competition in the aluminum alloy strip processing industry,it is dif-ficult to control the mass production of the same specifications,which is bound to affect the hot rolling production.This paper studied the effect of the hot rolling order of aluminum alloy on the surface quality of strip,such as roll printing,color difference,anodic oxidation,etc.,reasonable discharge sequence and corresponding optimization measures were formulated.展开更多
An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is ...An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is denoted by . Erdös, Faber and Lovász proposed a famous conjecture that holds for any loopless linear hypergraph H with n vertices. In this paper, we show that is true for gap-restricted hypergraphs. Our result extends a result of Alesandroni in 2021.展开更多
In this paper, using the properties of chromatic polynomial, we discuss the color-partition of the complement of lK 1∪(∪C u i),and characterize the graph with the same color-partition as the class graph under u...In this paper, using the properties of chromatic polynomial, we discuss the color-partition of the complement of lK 1∪(∪C u i),and characterize the graph with the same color-partition as the class graph under u i≠4k+2.展开更多
The chromatically uniqueness of bipartite graphs K (m, n) - A(]A] = 2) was studied. With comparing the numbers of partitions into r color classes of two chromatically equivalent graphs, one general numerical condi...The chromatically uniqueness of bipartite graphs K (m, n) - A(]A] = 2) was studied. With comparing the numbers of partitions into r color classes of two chromatically equivalent graphs, one general numerical condition guaranteeing that K( m, n) - A ( I A ] = 2) is chromatically unique were obtained. This covers and improves the former correlative results.展开更多
With its comprehensive application in network information engineering (e. g. dynamic spectrum allocation under different distance constraints ) and in network combination optimization (e. g. safe storage of deleter...With its comprehensive application in network information engineering (e. g. dynamic spectrum allocation under different distance constraints ) and in network combination optimization (e. g. safe storage of deleterious materials), the graphs' cloring theory and chromatic uniqueness theory have been the forward position of graph theory research. The later concerns the equivalent classification of graphs with their color polynomials and the determination of uniqueness of some equivalent classification under isomorphism. In this paper, by introducing the concept of chromatic normality and comparing the number of partitions of two chromatically equivalent graphs, a general numerical condition guarenteeing that bipartite graphs K ( m, n) - A (A belong to E(K (m, n) ) and | A |≥ 2) is chromatically unique was obtained and a lot of chromatic uniqueness graphs of bipartite graphs K(m, n) - A were determined. The results obtained in this paper were general. And the results cover and extend the majority of the relevant results obtained within the world.展开更多
In this paper, using the properties of chromatic polynomial, we discuss the color-partition of the complement of lK 1∪(∪C u i),and characterize the graph with the same color-partition as the class graph under u...In this paper, using the properties of chromatic polynomial, we discuss the color-partition of the complement of lK 1∪(∪C u i),and characterize the graph with the same color-partition as the class graph under u i≠4k+2.展开更多
In order to clean production of chromium compounds, it is a critical process to remove aluminates and utilize aluminum compounds from artificial chromate alkali solutions. The effects of Na2 Cr O4 on the neutralizatio...In order to clean production of chromium compounds, it is a critical process to remove aluminates and utilize aluminum compounds from artificial chromate alkali solutions. The effects of Na2 Cr O4 on the neutralization curve, Al(OH)3 precipitation efficiency and induction period of bayerite were investigated. The results indicate that the neutralization curve of the artificial chromate alkali solutions shows three distinct regions and its induction period is longer than that of pure sodium aluminate solutions at the same aluminum concentration. And the decreased temperature and volume fraction of CO2 enhance the particle size of bayerite β-Al(OH)3. Bayerite composed of agglomerates of rods and cone frustums was obtained from alkali metal chromate solutions with 28.5% CO2(volume fraction) at temperatures ranging from 50 °C to 70 °C. Coarse bayerite with particle size(d50) from 24.2 μm to 29.3 μm extremely has few impurities, which is suitable for comprehensive utilization.展开更多
The oxidizing roasting process of carbon ferrochrome to prepare potassium chromate in the presence of potassium carbonate and air was investigated. The effects of reaction temperature, reaction time, mole ratio of pot...The oxidizing roasting process of carbon ferrochrome to prepare potassium chromate in the presence of potassium carbonate and air was investigated. The effects of reaction temperature, reaction time, mole ratio of potassium carbonate to carbon ferrochrome were studied, and thermodynamics and kinetics were also discussed. It was observed that the reaction temperature and reaction time had a significant influence on the roasting reaction of carbon ferrochrome. The reaction mechanism changed greatly as the temperature varied. A two-stage roasting process was favorable for the roasting reaction, and a chromium recovery rate of 97.06% was obtained through this two-stage roasting method. The chromium residue yielded from this method was only 1/3 of the product. Moreover, the component of Fe in the residue was as high as 55.04%. Therefore, it can be easily recovered to produce sponge iron, realizing complete detoxication and zero-emission of chromium residue.展开更多
For the clean and economical production of chromium compounds, it is crucial to remove aluminates from chromate alkali solutions and utilize aluminum-containing compounds. In this work, carbonization was used to remov...For the clean and economical production of chromium compounds, it is crucial to remove aluminates from chromate alkali solutions and utilize aluminum-containing compounds. In this work, carbonization was used to remove aluminates from a synthetic chromate leaching solution containing a high K2O/Al2O3 mole ratio. The influence of reaction temperature, carbonization time, flow rate of carbon dioxide, and seed ratio on the precipitation of Al was investigated. The optimal output was obtained under the following experimental conditions: a reaction temperature of 50 °C, a carbonization time of 100 min, a carbon dioxide flow rate of 0.1 L/min, and a seed ratio of 1.0. Gibbsite was obtained following carbonization. The structure and morphology of the gibbsite were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), and laser particle size analyzer. The particle size distribution and morphology of the gibbsite were significantly influenced by the experimental conditions. The gibbsite had a mean particle size (d50) of 16.72μm. The thermal decomposition of the gibbsite was analyzed by XRD and the decomposition path was determined. The obtained coarseα-Al2O3 precipitate, which contains 0.08% Cr2O3 and 0.10% K2O, was suitable for subsequent utilization.展开更多
An objectifying system for color inspections of traditional Chinese medicine (CITCM) is developed. The entire system includes two parts : The hardware and the software. The hardware is an image acquiring device und...An objectifying system for color inspections of traditional Chinese medicine (CITCM) is developed. The entire system includes two parts : The hardware and the software. The hardware is an image acquiring device under a standard lighting condition, and it mainly includes a xenon lamp with color temperature of 5 500 K as light source, an integrating sphere used for diffusing light and a high resolution CCD camera. The software is used for digital image processing, and the procedure is divided into three steps. Firstly the skin/non-skin classifi- cation is performed by utilizing the threshold in chrominance channels of the RGB color space. Secondly, the fa- cial features are localized by using the image segmentation and coordinates sorting. Finally, the facial special re- gion(SR) corresponding to five internal organs is achieved by utilizing masks designed to take advantage of mor- phology. Subsequently, the chromaticity is calculated. The system is tested by taking 83 samples of 30 young and 53 elderly people. The experiment shows that there is significant difference of all SRs between the young and the elderly, and the system has better performance for objectifying research of CITCM.展开更多
An integer distance graph is a graph G(Z, D) with the integer set Z as vertexset, in which an edge joining two vertices u and v if and only if | u - v | ∈ D, where D is a setof natural numbers. Using a related theore...An integer distance graph is a graph G(Z, D) with the integer set Z as vertexset, in which an edge joining two vertices u and v if and only if | u - v | ∈ D, where D is a setof natural numbers. Using a related theorem in combinatorics and some conclusions known to us in thecoloring of the distance graph, the chromatic number _X(G) is determined in this paper that is ofthe distance graph G(Z, D) for some finite distance sets D containing {2, 3} with D = 4 andcontaining {2, 3, 5} with | D | = 5 by the method in which the combination of a few periodiccolorings.展开更多
A new regression algorithm of an adaptive reduced relevance vector machine is proposed to estimate the illumination chromaticity of an image for the purpose of color constancy. Within the framework of sparse Bayesian ...A new regression algorithm of an adaptive reduced relevance vector machine is proposed to estimate the illumination chromaticity of an image for the purpose of color constancy. Within the framework of sparse Bayesian learning, the algorithm extends the relevance vector machine by combining global and local kernels adaptively in the form of multiple kernels, and the improved locality preserving projection (LLP) is then applied to reduce the column dimension of the multiple kernel input matrix to achieve less training time. To estimate the illumination chromaticity, the algorithm is trained by fuzzy central values of chromaticity histograms of a set of images and the corresponding illuminants. Experiments with real images indicate that the proposed algorithm performs better than the support vector machine and the relevance vector machine while requiring less training time than the relevance vector machine.展开更多
文摘Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp+(r-1)^G(i) the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of (r - 1)G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp+(r-1)^G(i)∪(r - 1)K1 (1 ≤i≤p). Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.
基金supported in part by the National Key R&D Program of China (No. 2023YFA1606401)CAS Project for Young Scientists in Basic Research (No. YSBR-002)+3 种基金Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDB34000000)the NSFC (Nos. 12305126, 12135017, 12121005)the support from the Youth Innovation Promotion Association of the Chinese Academy of Sciences (No. 2021419)the support from the Yong Scholar of Regional Development,CAS (No.[2023]15)
文摘In conventional isochronous mass spectrometry(IMS)performed on a storage ring,the precision of mass measurements for short-lived nuclei depends on the accurate determination of the revolution times(T)of stored ions.However,the resolution of T inevitably deteriorates due to the magnetic rigidity spread of the ions,limiting the mass-resolving power.In this study,we used the betatron tunes Q(the number of betatron oscillations per revolution)of the ions and established a correlation between T and Q.From this correlation,T was transformed to correspond to a fixed Q with higher resolution.Using these transformed T values,the masses of ^(63)Ge,^(65)As,^(67)Se,and ^(71)Kr agreed well with the mass values measured using the newly developed IMS(Bρ-IMS).We also studied the systematics of Coulomb displacement energies(CDEs)and found that anomalous staggering in CDEs was eliminated using new mass values.This method of T transformation is highly effective for conventional IMS equipped with a single time-of-flight detector.
基金supported by Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“Spanning connectivity and supereulerian properties of graphs”(2022D01C410).
文摘For positive integers k and r,a(k,r)-coloring of graph G is a proper vertex k-coloring of G such that the neighbors of any vertex v∈V(G)receive at least min{d_(G)(v),r}different colors.The r-hued chromatic number of G,denoted χ_(r)(G),is the smallest integer k such that G admits a(k,r)-coloring.Let Q_(n) be the n-dimensional hypercube.For any integers n and r with n≥2 and 2≤r≤5,we investigated the behavior of χ_(r)(Q_(n)),and determined the exact value of χ_(2)(Q_(n))and χ_(3)(Q_(n))for all positive integers n.
基金sponsored by National Key Research and Development Program of China(2023YFC3504200)High Level Key Discipline Construction of Traditional Chinese Medicine(zyyzdxk-2023272).
文摘Background:In this study,we explored the effects of different processing methods on the quality of Polygonatum cyrtonema Hua(PC),and the role of Huangjiu in the processing procedure.Methods:The sensory characteristics of the crude product,steamed product,and wine-processed product of PC were described.The colorimeter was used to analyze the chromatic values of three different processed products on PC.At the same time,the contents of the water extract and alcohol extract were measured separately.The content of three different processing Polygonatum Polysaccharide(PCP)was determined using 0.2%anthrone-sulfuric acid.The correlation difference between the chromatic values and chemical composition of different PC products was analyzed using various analytical methods.Results:The surface colors gradually deepened,the sweetness increased,the viscosity strengthened,and the tongue-numbing sensation disappeared after PC processing.The contents of extract and L^(*) gradually decreased from the crude to the steamed to the wine-processed product,consistent with the pattern of surface color alteration.While,E^(*)ab gradually increased.The content of PCP was crude product>wine-processed product>steamed product.The results of multivariate statistical analysis showed that the samples processed for crude,steamed,and wine-processed product were clustered into three classes.The correlation analysis showed that L^(*)and E^(*)ab were highly significant positively correlated with the content of PCP,and a*was significantly negatively correlated with the content of PCP.Conclusion:The results showed that the wine-processed product had the best quality.The internal quality of the PC was correlated with its characteristics and chromatic value.In this study,we investigated the internal and external quality of three different products of PC in order to provide a reference for further research on the impact of different processing methods on PC quality,the standardization of PC processing,and the role of Huangjiu in the processing of PC.
文摘With the intensification of market competition in the aluminum alloy strip processing industry,it is dif-ficult to control the mass production of the same specifications,which is bound to affect the hot rolling production.This paper studied the effect of the hot rolling order of aluminum alloy on the surface quality of strip,such as roll printing,color difference,anodic oxidation,etc.,reasonable discharge sequence and corresponding optimization measures were formulated.
文摘An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is denoted by . Erdös, Faber and Lovász proposed a famous conjecture that holds for any loopless linear hypergraph H with n vertices. In this paper, we show that is true for gap-restricted hypergraphs. Our result extends a result of Alesandroni in 2021.
文摘In this paper, using the properties of chromatic polynomial, we discuss the color-partition of the complement of lK 1∪(∪C u i),and characterize the graph with the same color-partition as the class graph under u i≠4k+2.
基金Supported by the Natural Science Foundation of Jiangxi , China (No.0511006)
文摘The chromatically uniqueness of bipartite graphs K (m, n) - A(]A] = 2) was studied. With comparing the numbers of partitions into r color classes of two chromatically equivalent graphs, one general numerical condition guaranteeing that K( m, n) - A ( I A ] = 2) is chromatically unique were obtained. This covers and improves the former correlative results.
基金Natural Science Foundation of Fujian, China (No.S0650011)
文摘With its comprehensive application in network information engineering (e. g. dynamic spectrum allocation under different distance constraints ) and in network combination optimization (e. g. safe storage of deleterious materials), the graphs' cloring theory and chromatic uniqueness theory have been the forward position of graph theory research. The later concerns the equivalent classification of graphs with their color polynomials and the determination of uniqueness of some equivalent classification under isomorphism. In this paper, by introducing the concept of chromatic normality and comparing the number of partitions of two chromatically equivalent graphs, a general numerical condition guarenteeing that bipartite graphs K ( m, n) - A (A belong to E(K (m, n) ) and | A |≥ 2) is chromatically unique was obtained and a lot of chromatic uniqueness graphs of bipartite graphs K(m, n) - A were determined. The results obtained in this paper were general. And the results cover and extend the majority of the relevant results obtained within the world.
文摘In this paper, using the properties of chromatic polynomial, we discuss the color-partition of the complement of lK 1∪(∪C u i),and characterize the graph with the same color-partition as the class graph under u i≠4k+2.
基金Project(51125018)supported by the National Science Found for Distinguished Young Scholars of ChinaProject(2011BAC06B07)supported by the National Key Technologies R&D Program of China+2 种基金Project(2011AA060704)supported by the National Hi-tech Research and Development Program of ChinaProjects(51204153,21106167)supported by the National Natural Science Foundation of ChinaProjects(2012M510552,2013T60175)supported by Financial Grant from the China Postdoctoral Science Foundation
文摘In order to clean production of chromium compounds, it is a critical process to remove aluminates and utilize aluminum compounds from artificial chromate alkali solutions. The effects of Na2 Cr O4 on the neutralization curve, Al(OH)3 precipitation efficiency and induction period of bayerite were investigated. The results indicate that the neutralization curve of the artificial chromate alkali solutions shows three distinct regions and its induction period is longer than that of pure sodium aluminate solutions at the same aluminum concentration. And the decreased temperature and volume fraction of CO2 enhance the particle size of bayerite β-Al(OH)3. Bayerite composed of agglomerates of rods and cone frustums was obtained from alkali metal chromate solutions with 28.5% CO2(volume fraction) at temperatures ranging from 50 °C to 70 °C. Coarse bayerite with particle size(d50) from 24.2 μm to 29.3 μm extremely has few impurities, which is suitable for comprehensive utilization.
基金Project(2009GK2003)supported by the Natural Science Foundation of Hunan Province,China
文摘The oxidizing roasting process of carbon ferrochrome to prepare potassium chromate in the presence of potassium carbonate and air was investigated. The effects of reaction temperature, reaction time, mole ratio of potassium carbonate to carbon ferrochrome were studied, and thermodynamics and kinetics were also discussed. It was observed that the reaction temperature and reaction time had a significant influence on the roasting reaction of carbon ferrochrome. The reaction mechanism changed greatly as the temperature varied. A two-stage roasting process was favorable for the roasting reaction, and a chromium recovery rate of 97.06% was obtained through this two-stage roasting method. The chromium residue yielded from this method was only 1/3 of the product. Moreover, the component of Fe in the residue was as high as 55.04%. Therefore, it can be easily recovered to produce sponge iron, realizing complete detoxication and zero-emission of chromium residue.
基金Project(51125018)supported by the National Science Foundation for Distinguished Young Scholars of ChinaProject(2011AA060704)supported by the National High-tech Research and Development Program of ChinaProjects(51204153,21406246)supported by the National Natural Science Foundation of China
文摘For the clean and economical production of chromium compounds, it is crucial to remove aluminates from chromate alkali solutions and utilize aluminum-containing compounds. In this work, carbonization was used to remove aluminates from a synthetic chromate leaching solution containing a high K2O/Al2O3 mole ratio. The influence of reaction temperature, carbonization time, flow rate of carbon dioxide, and seed ratio on the precipitation of Al was investigated. The optimal output was obtained under the following experimental conditions: a reaction temperature of 50 °C, a carbonization time of 100 min, a carbon dioxide flow rate of 0.1 L/min, and a seed ratio of 1.0. Gibbsite was obtained following carbonization. The structure and morphology of the gibbsite were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), and laser particle size analyzer. The particle size distribution and morphology of the gibbsite were significantly influenced by the experimental conditions. The gibbsite had a mean particle size (d50) of 16.72μm. The thermal decomposition of the gibbsite was analyzed by XRD and the decomposition path was determined. The obtained coarseα-Al2O3 precipitate, which contains 0.08% Cr2O3 and 0.10% K2O, was suitable for subsequent utilization.
基金Supported by the Innovation Team Fund of Nanjing University of Aeronautics and Astronauticsthe Chinese Medical Association Research Project(S10)~~
文摘An objectifying system for color inspections of traditional Chinese medicine (CITCM) is developed. The entire system includes two parts : The hardware and the software. The hardware is an image acquiring device under a standard lighting condition, and it mainly includes a xenon lamp with color temperature of 5 500 K as light source, an integrating sphere used for diffusing light and a high resolution CCD camera. The software is used for digital image processing, and the procedure is divided into three steps. Firstly the skin/non-skin classifi- cation is performed by utilizing the threshold in chrominance channels of the RGB color space. Secondly, the fa- cial features are localized by using the image segmentation and coordinates sorting. Finally, the facial special re- gion(SR) corresponding to five internal organs is achieved by utilizing masks designed to take advantage of mor- phology. Subsequently, the chromaticity is calculated. The system is tested by taking 83 samples of 30 young and 53 elderly people. The experiment shows that there is significant difference of all SRs between the young and the elderly, and the system has better performance for objectifying research of CITCM.
文摘An integer distance graph is a graph G(Z, D) with the integer set Z as vertexset, in which an edge joining two vertices u and v if and only if | u - v | ∈ D, where D is a setof natural numbers. Using a related theorem in combinatorics and some conclusions known to us in thecoloring of the distance graph, the chromatic number _X(G) is determined in this paper that is ofthe distance graph G(Z, D) for some finite distance sets D containing {2, 3} with D = 4 andcontaining {2, 3, 5} with | D | = 5 by the method in which the combination of a few periodiccolorings.
基金The National Natural Science Foundation of China(No60573139)the Innovation Foundation of Xidian University forGraduates (No05008)
文摘A new regression algorithm of an adaptive reduced relevance vector machine is proposed to estimate the illumination chromaticity of an image for the purpose of color constancy. Within the framework of sparse Bayesian learning, the algorithm extends the relevance vector machine by combining global and local kernels adaptively in the form of multiple kernels, and the improved locality preserving projection (LLP) is then applied to reduce the column dimension of the multiple kernel input matrix to achieve less training time. To estimate the illumination chromaticity, the algorithm is trained by fuzzy central values of chromaticity histograms of a set of images and the corresponding illuminants. Experiments with real images indicate that the proposed algorithm performs better than the support vector machine and the relevance vector machine while requiring less training time than the relevance vector machine.